/*

 * jidctfst.c

 *

 * Copyright (C) 1994-1998, Thomas G. Lane.

 * Modified 2015-2017 by Guido Vollbeding.

 * This file is part of the Independent JPEG Group's software.

 * For conditions of distribution and use, see the accompanying README file.

 *

 * This file contains a fast, not so accurate integer implementation of the

 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine

 * must also perform dequantization of the input coefficients.

 *

 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT

 * on each row (or vice versa, but it's more convenient to emit a row at

 * a time).  Direct algorithms are also available, but they are much more

 * complex and seem not to be any faster when reduced to code.

 *

 * This implementation is based on Arai, Agui, and Nakajima's algorithm for

 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in

 * Japanese, but the algorithm is described in the Pennebaker & Mitchell

 * JPEG textbook (see REFERENCES section in file README).  The following code

 * is based directly on figure 4-8 in P&M.

 * While an 8-point DCT cannot be done in less than 11 multiplies, it is

 * possible to arrange the computation so that many of the multiplies are

 * simple scalings of the final outputs.  These multiplies can then be

 * folded into the multiplications or divisions by the JPEG quantization

 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds

 * to be done in the DCT itself.

 * The primary disadvantage of this method is that with fixed-point math,

 * accuracy is lost due to imprecise representation of the scaled

 * quantization values.  The smaller the quantization table entry, the less

 * precise the scaled value, so this implementation does worse with high-

 * quality-setting files than with low-quality ones.

 */

#define JPEG_INTERNALS

#include "jinclude.h"

#include "jpeglib.h"

#include "jdct.h"   /* Private declarations for DCT subsystem */

#ifdef DCT_IFAST_SUPPORTED

/*

 * This module is specialized to the case DCTSIZE = 8.

 */

#if DCTSIZE != 8

  Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */

#endif

/* Scaling decisions are generally the same as in the LL&M algorithm;

 * see jidctint.c for more details.  However, we choose to descale

 * (right shift) multiplication products as soon as they are formed,

 * rather than carrying additional fractional bits into subsequent additions.

 * This compromises accuracy slightly, but it lets us save a few shifts.

 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)

 * everywhere except in the multiplications proper; this saves a good deal

 * of work on 16-bit-int machines.

 *

 * The dequantized coefficients are not integers because the AA&N scaling

 * factors have been incorporated.  We represent them scaled up by PASS1_BITS,

 * so that the first and second IDCT rounds have the same input scaling.

 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to

 * avoid a descaling shift; this compromises accuracy rather drastically

 * for small quantization table entries, but it saves a lot of shifts.

 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,

 * so we use a much larger scaling factor to preserve accuracy.

 *

 * A final compromise is to represent the multiplicative constants to only

 * 8 fractional bits, rather than 13.  This saves some shifting work on some

 * machines, and may also reduce the cost of multiplication (since there

 * are fewer one-bits in the constants).

 */

#if BITS_IN_JSAMPLE == 8

#define CONST_BITS  8

#define PASS1_BITS  2

#else

#define CONST_BITS  8

#define PASS1_BITS  1   /* lose a little precision to avoid overflow */

#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus

 * causing a lot of useless floating-point operations at run time.

 * To get around this we use the following pre-calculated constants.

 * If you change CONST_BITS you may want to add appropriate values.

 * (With a reasonable C compiler, you can just rely on the FIX() macro...)

 */

#if CONST_BITS == 8

#define FIX_1_082392200  ((INT32)  277)   /* FIX(1.082392200) */

#define FIX_1_414213562  ((INT32)  362)   /* FIX(1.414213562) */

#define FIX_1_847759065  ((INT32)  473)   /* FIX(1.847759065) */

#define FIX_2_613125930  ((INT32)  669)   /* FIX(2.613125930) */

#else

#define FIX_1_082392200  FIX(1.082392200)

#define FIX_1_414213562  FIX(1.414213562)

#define FIX_1_847759065  FIX(1.847759065)

#define FIX_2_613125930  FIX(2.613125930)

#endif

/* We can gain a little more speed, with a further compromise in accuracy,

 * by omitting the addition in a descaling shift.  This yields an incorrectly

 * rounded result half the time...

 */

#ifndef USE_ACCURATE_ROUNDING

#undef DESCALE

#define DESCALE(x,n)  RIGHT_SHIFT(x, n)

#endif

/* Multiply a DCTELEM variable by an INT32 constant, and immediately

 * descale to yield a DCTELEM result.

 */

#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))

/* Dequantize a coefficient by multiplying it by the multiplier-table

 * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16

 * multiplication will do.  For 12-bit data, the multiplier table is

 * declared INT32, so a 32-bit multiply will be used.

 */

#if BITS_IN_JSAMPLE == 8

#define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval))

#else

#define DEQUANTIZE(coef,quantval)  \

  DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)

#endif

/*

 * Perform dequantization and inverse DCT on one block of coefficients.

 *

 * cK represents cos(K*pi/16).

 */

GLOBAL(void)

jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,

     JCOEFPTR coef_block,

     JSAMPARRAY output_buf, JDIMENSION output_col)

{

  DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  DCTELEM tmp10, tmp11, tmp12, tmp13;

  DCTELEM z5, z10, z11, z12, z13;

  JCOEFPTR inptr;

  IFAST_MULT_TYPE * quantptr;

  int * wsptr;

  JSAMPROW outptr;

  JSAMPLE *range_limit = IDCT_range_limit(cinfo);

  int ctr;

  int workspace[DCTSIZE2];  /* buffers data between passes */

  SHIFT_TEMPS     /* for DESCALE */

  ISHIFT_TEMPS      /* for IRIGHT_SHIFT */

  /* Pass 1: process columns from input, store into work array. */

  inptr = coef_block;

  quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;

  wsptr = workspace;

  for (ctr = DCTSIZE; ctr > 0; ctr--) {

    /* Due to quantization, we will usually find that many of the input

     * coefficients are zero, especially the AC terms.  We can exploit this

     * by short-circuiting the IDCT calculation for any column in which all

     * the AC terms are zero.  In that case each output is equal to the

     * DC coefficient (with scale factor as needed).

     * With typical images and quantization tables, half or more of the

     * column DCT calculations can be simplified this way.

     */

    if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&

  inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&

  inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&

  inptr[DCTSIZE*7] == 0) {

      /* AC terms all zero */

      int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

      wsptr[DCTSIZE*0] = dcval;

      wsptr[DCTSIZE*1] = dcval;

      wsptr[DCTSIZE*2] = dcval;

      wsptr[DCTSIZE*3] = dcval;

      wsptr[DCTSIZE*4] = dcval;

      wsptr[DCTSIZE*5] = dcval;

      wsptr[DCTSIZE*6] = dcval;

      wsptr[DCTSIZE*7] = dcval;

      inptr++;      /* advance pointers to next column */

      quantptr++;

      wsptr++;

      continue;

    }

    /* Even part */

    tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

    tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);

    tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

    tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

    tmp10 = tmp0 + tmp2;  /* phase 3 */

    tmp11 = tmp0 - tmp2;

    tmp13 = tmp1 + tmp3;  /* phases 5-3 */

    tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */

    tmp0 = tmp10 + tmp13; /* phase 2 */

    tmp3 = tmp10 - tmp13;

    tmp1 = tmp11 + tmp12;

    tmp2 = tmp11 - tmp12;

    /* Odd part */

    tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

    tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);

    tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);

    tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);

    z13 = tmp6 + tmp5;    /* phase 6 */

    z10 = tmp6 - tmp5;

    z11 = tmp4 + tmp7;

    z12 = tmp4 - tmp7;

    tmp7 = z11 + z13;   /* phase 5 */

    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */

    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */

    tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */

    tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */

    tmp6 = tmp12 - tmp7;  /* phase 2 */

    tmp5 = tmp11 - tmp6;

    tmp4 = tmp10 - tmp5;

    wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);

    wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);

    wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);

    wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);

    wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);

    wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);

    wsptr[DCTSIZE*3] = (int) (tmp3 + tmp4);

    wsptr[DCTSIZE*4] = (int) (tmp3 - tmp4);

    inptr++;      /* advance pointers to next column */

    quantptr++;

    wsptr++;

  }

  /* Pass 2: process rows from work array, store into output array.

   * Note that we must descale the results by a factor of 8 == 2**3,

   * and also undo the PASS1_BITS scaling.

   */

  wsptr = workspace;

  for (ctr = 0; ctr < DCTSIZE; ctr++) {

    outptr = output_buf[ctr] + output_col;

    /* Add range center and fudge factor for final descale and range-limit. */

    z5 = (DCTELEM) wsptr[0] +

     ((((DCTELEM) RANGE_CENTER) << (PASS1_BITS+3)) +

      (1 << (PASS1_BITS+2)));

    /* Rows of zeroes can be exploited in the same way as we did with columns.

     * However, the column calculation has created many nonzero AC terms, so

     * the simplification applies less often (typically 5% to 10% of the time).

     * On machines with very fast multiplication, it's possible that the

     * test takes more time than it's worth.  In that case this section

     * may be commented out.

     */

#ifndef NO_ZERO_ROW_TEST

    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&

  wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {

      /* AC terms all zero */

      JSAMPLE dcval = range_limit[(int) IRIGHT_SHIFT(z5, PASS1_BITS+3)

          & RANGE_MASK];

      outptr[0] = dcval;

      outptr[1] = dcval;

      outptr[2] = dcval;

      outptr[3] = dcval;

      outptr[4] = dcval;

      outptr[5] = dcval;

      outptr[6] = dcval;

      outptr[7] = dcval;

      wsptr += DCTSIZE;   /* advance pointer to next row */

      continue;

    }

#endif

    /* Even part */

    tmp10 = z5 + (DCTELEM) wsptr[4];

    tmp11 = z5 - (DCTELEM) wsptr[4];

    tmp13 = (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6];

    tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6],

         FIX_1_414213562) - tmp13; /* 2*c4 */

    tmp0 = tmp10 + tmp13;

    tmp3 = tmp10 - tmp13;

    tmp1 = tmp11 + tmp12;

    tmp2 = tmp11 - tmp12;

    /* Odd part */

    z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];

    z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];

    z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];

    z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];

    tmp7 = z11 + z13;   /* phase 5 */

    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */

    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */

    tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */

    tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */

    tmp6 = tmp12 - tmp7;  /* phase 2 */

    tmp5 = tmp11 - tmp6;

    tmp4 = tmp10 - tmp5;

    /* Final output stage: scale down by a factor of 8 and range-limit */

    outptr[0] = range_limit[(int) IRIGHT_SHIFT(tmp0 + tmp7, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[7] = range_limit[(int) IRIGHT_SHIFT(tmp0 - tmp7, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[1] = range_limit[(int) IRIGHT_SHIFT(tmp1 + tmp6, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[6] = range_limit[(int) IRIGHT_SHIFT(tmp1 - tmp6, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[2] = range_limit[(int) IRIGHT_SHIFT(tmp2 + tmp5, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[5] = range_limit[(int) IRIGHT_SHIFT(tmp2 - tmp5, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[3] = range_limit[(int) IRIGHT_SHIFT(tmp3 + tmp4, PASS1_BITS+3)

          & RANGE_MASK];

    outptr[4] = range_limit[(int) IRIGHT_SHIFT(tmp3 - tmp4, PASS1_BITS+3)

          & RANGE_MASK];

    wsptr += DCTSIZE;   /* advance pointer to next row */

  }

}

#endif /* DCT_IFAST_SUPPORTED */